Stats test 3

What is the conceptual similarity between all the different Sum of Squares we have discussed this semester?

---------------- See notebook

You will need to identify the appropriate statistical technique for analyzing data in research scenarios I provide.

See name that statistic

Describe the basic logic of ANOVA.

ANOVA is based on the ratio of within group variability and between groups variability. Within: obtained by averaging the standard deviations of each of the three groups. Good measure of individual variability Between: comparing the individual group means to the grand mean. Means of the group may differ due to a treatment effect or individual differences

Know the advantages and disadvantages of using the repeated measures approach to research design. What are the advantages and disadvantages of the between groups design?

Advantages: The repeated sample t requires fewer subjects than independent measures. Better suited for studying changes over time The individual differences is minimized Disadvantages: Carry over effect where the pretest can influence their scores on the post test Since the subjects must be measured twice, this will be more difficult and time consuming The adv and disad of between groups is just the flip of repeated measures.

Make sure you understand the interrelationships between sum of squares, degrees of freedom, mean squares, and F in the ANOVA summary table.

All the formulas

What does acronym ANOVA stand for?

Analysis of Variance

What is the difference between a Between Group research design and a Within Group research design?

Between groups: two different groups of subjects are compared Within group: The same group of subjects are measured twice (pre-test and post-test)

What is the formula for degrees of freedom between? What is the formula for degrees of freedom within?

Between: J-1 where J is the number of groups Within: N-J where N is the total number of subjects

Distinguish between Completely between and Mixed factorial designs

Completely between: different subjects in each group Mixed: at least one between groups factor and one within groups factor. Remember, a between groups factor compares different groups of subjects and a within groups factor is when repeated measures are taken on the same subjects

In the context of the one sample t statistic, what are degrees of freedom?

Degrees of freedom are the number of components in the calculation of a statistic that are free to vary. Calculate a mean: N-1 Calculate a statistic comparing a treatment and control group: N-2

You will be asked to interpret the results of a 2x2 completely between factorial ANOVA using SPSS output. Be sure you know how to evaluate main effects as well as draw and interpret interactions

F (1,36) = 14.00, p = .000 The Main Effect of Drug is Significant- Individual who took Drowsen fell asleep significantly faster than individuals that took the Placebo F (1,36) = 5.74, p = .022 The Main Effect of Experience is Significant- Individuals with no experience with the drug fell asleep significantly sooner than chronic Drowesen users A synergistic interaction since the there was virtually no difference between No Experience and Chronic users in the Placebo condition, but a large difference in the Drowsen condition

Know the basic terminology of Factorial designs. What is a Factor? What are levels? What is a main effect? What is an interaction?

Factor: independent or subject variable Level: groups within a factor. Ex: if gender was the factor then male and female would be the levels Main effect: effect of one factor averaging over the levels of a second factor Interaction: occurs when the effect of one factor depends on the level of a second factor

What are Factorial Designs?

Factorial designs are designs with two or more independent/ subject variables

What is the purpose of post hoc tests?

If a significant F value is found, then we must determine which of the group means are significantly different from one another

Draw the sampling distribution of F.

Most frequently occurring value of F is 1 There also will not be a negative value for F since its a ratio of two variances

As the value of t gets smaller, what happens to the value of p?

P gets larger. Check notebook

Repeated meausres advantages and disadvantages compared to between groups advantages and disadvantages.

Repeated measures: Advantages 1.More sensitive to treatment effects 2. Measure change over time 3. Fewer subjects Disadvantages 1. Carry over effects of pre test and post test 2. More time consuming

What value would we expect for the Independent and Repeated measures t tests if the null hypothesis is true?

Repeated measures: If the null hypothesis is true, then we will expect the mean of the difference scores in the population will equal 0. Independent t test: We would expect the mean of the treatment group to equal the mean of the control group. So in the numerator it would be "5-5" so we would expect 0

What are the degrees of freedom for the independent t test? What about the repeated measures t?

Repeated measures: N-1 where N= the number of pairs of scores Independent t test: N-2 where N= the number of subjects in the experiment. Independent sample t uses 2 standard deviations so we lose one degree of freedom.

What is the difference between the one sample z test and the one sample t test?

The denominator of the statistic is different. The one sample t test uses the standard deviation of the sample as an estimate of the population standard deviation. The z statistic uses the standard deviation of the population.

Conceptually, what does the F ratio represent?

The f ratio is a measure of the treatment effect

What is the conceptual similarity between mean squares and the variance (s^2)

The mean squares and the variance are both the sum of squares divided by degrees of freedom

You will be asked to interpret the results of a one way ANOVA analysis using SPSS output

There is a significant treatment effect: F(2,27) = 18.97, p=.000 *There was not a significant difference in the number of words recalled in the physical and rhyme conditions. However, subjects in the content condition recalled significantly more words compared to subjects in the physical and rhyme conditions

How are the conceptual formulas for the Independent and Repeated samples t tests similar/different?

There is less variability in the denominator of the releated measures t test. The repeated measures test is more similar to a one sample t test.

What is the relationship between the shape of the sampling distribution of T and sample size?

They are directly proportional

When do we use a one sample t test?

Use one sample t test when comparing your sample mean to a population mean and you don't know the standard deviation of the population.

What is the conceptual formula for the repeated measures t test?

Use the second one

What is actually measured by sum of squares between?

We are comparing each individual group mean to the grand mean

What is actually measured by sum of squares within?

We are comparing each individual score to their own group mean

Give an example of a research design where One Way ANOVA would be the appropriate statistical technique for analysis

We use ANOVA when we have 1 independent variable and 3 or more groups Example: three groups are tested for reaction time before alcohol is consumed and then at moderate and high consumptions

What value for F would we expect if the null hypothesis is true? Explain why this number would be the expected value.

We would expect all positive numbers because F is a ratio of two squared numbers. We would also expect, on average, 1 to be the most frequently occurring value This is also represented in the sampling distribution model

You will need to describe Factorial experiments using factorial notation (e.g. 2x2 mixed factorial). Also be prepared to draw a factorial matrix of a design describe in factorial notation

____ X ____ indicates the number of Factors. First number is the amount of columns and second number is amount of rows So a 3x2= xxx xxx